3^2x=27^4/3

Solution for 3^2x=27^4/3 equation:

3^2x=27^4/3

We move all terms to the left:

3^2x-(27^4/3)=0

We get rid of parentheses

3^2x-27^4/3=0

We multiply all the terms by the denominator


3^2x*3-27^4=0

We add all the numbers together, and all the variables

3^2x*3-531441=0

Wy multiply elements

9x^2-531441=0

a = 9; b = 0; c = -531441;
Δ = b2-4ac
Δ = 02-4·9·(-531441)
Δ = 19131876
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{19131876}=4374$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4374}{2*9}=\frac{-4374}{18}
=-243
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4374}{2*9}=\frac{4374}{18}
=243
$